CBS News reporter Bob Simon and his three-man crew, who disappeared in the Saudi desert last month, have been held in Baghdad for two weeks, CNN reported Friday.

The crew was reported missing at the Kuwaiti border on Jan. 21, four days after the war started. CNN quoted what it called reliable sources as saying the fate of the crew would be decided by Saddam Hussein.The four were picked up by an Iraqi military patrol in a remote part of the Kuwait border, said CNN correspondent Peter Arnett.

They "are still being investigated by the Iraqi intelligence service to determine the full circumstances of their capture," he said.

Arnett said that, "apparently, there are three categories they can fall under: Innocents who could be released, prisoners of war or spies.

Three of the crew were wearing military uniforms to pass by Saudi checkpoints in the guise of American soldiers, Arnett said he was told.

Along with Simon, the missing crew members are producer Peter Bluff, cameraman Roberto Alvarez and soundman Juan Caldera.